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    "# first I am going to import the needed libraries. Only numpy in this case since there is nothing to plot\n",
    "import numpy as np\n",
    "# here I write a function that takes an integer as input and returns an array with all the prime factors\n",
    "def primFact(n):\n",
    "# first I create the empty array where to store the prome factors\n",
    "    result=np.array([])\n",
    "# then I create an array with all the number I want to check. \n",
    "# This is not very efficient since in principles I need to check only primes.\n",
    "    numTest=np.arange(2,n,1)\n",
    "# now I cycle over al the numbers I am testing    \n",
    "    for nt in numTest:\n",
    "# I use a while loop here since the same prime number may appear multiple times.\n",
    "# the while loop runs as long as it finds that the remainder of the division is 0.\n",
    "        while n%nt==0:\n",
    "# If the remainder of the division is zero, the number tested is added to the array of results\n",
    "            result=np.append(result,nt)\n",
    "# the input number is now divided by the found divisor\n",
    "            n=n/nt\n",
    "# when all numbers have been tested, the result is returned\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please enter the first integer number 756\n",
      "The number you entered, rounded to integer, is: 756\n",
      "The prime decomposition of your input number is: [2. 2. 3. 3. 3. 7.]\n",
      "Please enter the second integer number 5040\n",
      "The number you entered, rounded to integer, is: 5040\n",
      "The prime decomposition of your input number is: [2. 2. 2. 2. 3. 3. 5. 7.]\n"
     ]
    }
   ],
   "source": [
    "# This line requires the input number, turns it into a float, and then into an integer, \n",
    "# just in case it was entered as a real\n",
    "num1=int(float(input('Please enter the first integer number ')))\n",
    "# Then the number is printed back to ensure accuracy\n",
    "print('The number you entered, rounded to integer, is:',num1)\n",
    "# The routine above is called to obtain the factorization\n",
    "pf1=primFact(num1)\n",
    "# The result is printed out\n",
    "print('The prime decomposition of your input number is:',pf1)\n",
    "# SAme as above for the second number\n",
    "num2=int(float(input('Please enter the second integer number ')))\n",
    "# more of the same\n",
    "print('The number you entered, rounded to integer, is:',num2)\n",
    "# more of the same\n",
    "pf2=primFact(num2)\n",
    "# printing out the result\n",
    "print('The prime decomposition of your input number is:',pf2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum common divisor is: 252.0\n"
     ]
    }
   ],
   "source": [
    "# sets the initial guess of the MCD as 1. This is the smallest possible value that an MCD can be\n",
    "mcd=1\n",
    "# now the code cycles over all teh prime factors of the first number (could have been the second)\n",
    "for n in pf1:\n",
    "# this is a command that finds all locations where n (a factor of pf1) appears in pf2\n",
    "    jj=np.where(pf2==n)\n",
    "# if it appears, then the MCD is multiplied by n\n",
    "    if jj[0].size>0:\n",
    "        mcd=mcd*n\n",
    "# that number is now removed from pf2 since it has been used.\n",
    "        pf2[jj[0][0]]=-1\n",
    "# the final result is printed out\n",
    "print('The maximum common divisor is:',mcd)"
   ]
  },
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   "execution_count": null,
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